How to compute characteristic polynominal of two conics

Question

If I have two conics defined as $A: XAX^T$ and $B: XBX^T$ how can I expand characteristic polynomial $f(\lambda) = det(\lambda A + B) $ so that it can be computed by a computer program or Matlab?

Answer 1

Most maths programs are able to calculate the determinant of a matrix. Especially MatLab (Matrix Laboratory).

Use "x = sym('x')" for symbolic calculations.

Eg:

x = sym('x');

A = eye(3);

B = [1,2,3;4,5,6;7,8,9];

det(A*x + B)

Output will be : $$x^3 + 15x^2 - 18x$$